Directed force chain networks and stress response in static granular materials

A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general Boltzmann equation for the densities of force chains in different directions is proposed and a complete solution is obtained for a special case in which chains lie along a d...

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Bibliographic Details
Published in:The European physical journal. E, Soft matter and biological physics Soft matter and biological physics, 2002-04, Vol.7 (4), p.353-370
Main Authors: Socolar, J E S, Schaeffer, D G, Claudin, P
Format: Article
Language:English
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Summary:A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general Boltzmann equation for the densities of force chains in different directions is proposed and a complete solution is obtained for a special case in which chains lie along a discrete set of directions. The analysis and results demonstrate the necessity of including nonlinear terms in the Boltzmann equation. A line of nontrivial fixed-point solutions is shown to govern the properties of large systems. In the vicinity of a generic fixed point, the response to a localized load shows a crossover from a single, centered peak at intermediate depths to two propagating peaks at large depths that broaden diffusively.
ISSN:1292-8941
1292-895X
DOI:10.1140/epje/i2002-10011-7